Born in Fujian, China, Lin graduated from the National Tsing Hua University on Taiwan. He then obtained his MA from the University of Toronto in 1941 and his PhD in 1944 from the California Institute of Technology, Pasadena. After teaching briefly at Brown University, Rhode Island (1945–47), he moved to the Massachusetts Institute of Technology. He was appointed professor of applied mathematics in 1953, becoming Institute Professor in 1966.

Lin worked on problems of hydrodynamics and turbulent flow in general. At a more particular level he was considered and was widely known for his account of how the spiral structure of spiral galaxies is sustained. Lin's account, known as the ‘density-wave theory,’ is based on work by Bertil Lindblad and was worked out in collaboration with Frank Shu in 1964.

They proposed that the spiral structure is a rotating density wave that sweeps through the galaxy. The spiral pattern is always there but the material in the pattern is continuously changing under the influence of gravity. It is further supposed that as the spiral wave moves through a region it compresses the gas there sufficiently to trigger the process of star formation along the lines of compression. Young stars should therefore be found in the arms of a spiral galaxy, as indeed they are. The model has received some additional observational support by predicting that spiral arms must trail and cannot lead as the galaxy rotates. Its universality has, however, been challenged by H. Gerola and P. Seiden who proposed in 1977 an alternative mechanism triggered by supernovae, without needing to assume the presence of an underlying density wave.